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Dictyostelium discoideumslugs show a pronounced thermotaxis. We have modelled the motion of the D. discoideumslug in the absence and in the presence of a thermal gradient. Our model is an extension of the hybrid cellular automata/partial differential equation model, as formulated by Savill and Hogeweg [J. theor. Biol., (1997) 184, 229–235]. The modelled slugs maintain their shape and crawl, with a velocity depending on slug size, as found in experiments. Moreover, they show thermotactic behaviour: independent of the initial orientation, after some transient process, the slugs start moving along the temperature gradient. The slug behaviour in our model is due to the collective behaviour of the amoebae. Individual amoebae can neither respond to a shallow temperature gradient, nor show differentiation in motion velocity. The behaviour is achieved by a modification of the cyclic AMP waves: differences in temperature alter the excitability of the cell, and thereby the shape of the cyclic AMP wave. Chemotaxis towards cyclic AMP causes the slug to turn. We show that the mechanism still functions at very low signal-to-noise ratios.